Related papers: A note on a paper by Wong and Heyde

This note addresses issues raised by Cox and Reid in their seminal paper in 1987 regarding parameter orthogonality in statistical inference. We extend the orthogonality condition to cases with multiple parameters of interest and demonstrate…

Rejoinder to ``Equi-energy sampler with applications in statistical inference and statistical mechanics'' by Kou, Zhou and Wong [math.ST/0507080]

This is an overview of the area of Stochastic Portfolio Theory, and can be seen as an updated and extended version of the survey paper by Fernholz and Karatzas (Handbook of Numerical Analysis Vol.15:89-167, 2009).

We formulate and prove a generalization of Hardy's inequality (Hardy,1925) in terms of random variables and show that it contains the usual (or familiar) continuous and discrete forms of Hardy's inequality. Next we improve the recent…

In this paper we further study the stochastic partial differential equation first proposed by Xiong (2013). Under localized conditions on the coefficients we show that the solution is in fact distribution-function-valued and we establish…

This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors.

We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a…

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…

We improve upon the majorant estimates introduced by Mockenhaupt and Schlag by applying Bourgain's $\Lambda(p)$ property to random sets.

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pe\~{n}a. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated…

This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…

The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$) and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$ ($p\in (1, \infty)$)…

In this paper we study the path-regularity and martingale properties of the set-valued stochastic integrals defined in our previous work Ararat et al. (2023). Such integrals have some fundamental differences from the well-known…

The paper presents a counterexample to the Hodge conjecture.

The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…

Starting from the seventies mathematicians face the question whether a non-negative local martingale is a true or a strict local martingale. In this article we answer this question from a semimartingale perspective. We connect the…

In this note, we give the possible revised version of the unique solvability conditions for the two incorrect results that appeared in the published paper by Wu et al. (Appl Math Lett 76:195-200, 2018).

We construct a pathwise calculus for functionals of integer-valued measures and use it to derive an martingale representation formula with respect to a large class of integer-valued random measures. Using these results, we extend the…

The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…

This is a revision and update of the part of the preprint math.CO/0405210 concerning field coefficients, line complexes, and the Hessian arrangement. The material from that paper concerning coefficients in arbitrary commutative rings and…